Vibrations and Waves · Problem 1-7

The superposition of periodic motions — A.P. French

Physics — Waves · complex-exponential

Problem

(a) Justify the formulas cos⁡θ=(ejθ+e−jθ)/2\cos\theta = (e^{j\theta} + e^{-j\theta})/2 and sin⁡θ=(ejθ−e−jθ)/2j\sin\theta = (e^{j\theta} - e^{-j\theta})/2j, using the appropriate series. (b) Display the above relationships geometrically by means of vector diagrams in the xyxy plane.

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